Zero-Branes on a Compact Orbifold

TL;DR

This paper explores the algebraic structure of zero-branes on a compact orbifold, revealing a unified description of their moduli spaces and connections to dualities, instantons, and AdS/CFT correspondence.

Contribution

It introduces a non-commutative algebra framework for zero-branes on $T^4/Z_2$, unifying moduli spaces and linking them to dualities and instanton properties.

Findings

Unified description of zero-brane, two-brane, and four-brane moduli spaces.

Identification of fixed points with six-dimensional scale in degenerate limits.

Evidence for branes' placement in AdS space via the large N limit of the (0,2) theory.

Abstract

The non-commutative algebra which defines the theory of zero-branes on $T^4/Z_2$ allows a unified description of moduli spaces associated with zero-branes, two-branes and four-branes on the orbifold space. Bundles on a dual space $\hat T^4/Z_2$ play an important role in this description. We discuss these moduli spaces in the context of dualities of K3 compactifications, and in terms of properties of instantons on $T^4$. Zero-branes on the degenerate limits of the compact orbifold lead to fixed points with six-dimensional scale but not conformal invariance. We identify some of these in terms of the ADS dual of the $(0,2)$ theory at large $N$, giving evidence for an interesting picture of "where the branes live" in ADS.